System for testing electric signal transfer devices



Jung-2, r1960 n s. 1;' KRAMER 2,942,182

SYSTEM FOR TESTING ELECTRIC SIGNAL TRANSFER DEVICES Filed oct. 5, 195e 2 sheets-sheet 1 Llj 0 :e no u (ira) 70 x'p 0 g @D "l" E o 21/ Flasc.

FIG

FIGA

O N d' E Il) n a q) O3 LD C) E INVEN-roa STANLEY KRAMER LI.- Malina-L74 (l. Ir 7 im e our S. I. KRAMER June 21, `1960 SYSTEM FOR TESTING ELECTRIC SIGNAL TRANSFER DEVICES Filed oct. 3, 195e 2 SheetsSheet 2 In N .1 I I I I I l I l I I I I l I I I I I I I I l I I I I I I I I I I I I I I I I I I I I I I I I I I l I I I I I I I l I INVENTOR STANLEY KRAMER BY l 4M. duna H ATTORNEYS United States Patent C SYSTEM EoR TESTING ELECTRIC SIGNAL TRANSFER DEVICES Stanley I. Kramer, Brightwaters, N.Y., assgnor to Fairchild Engine'and Airplane Corporation, Hagerstown, Md., a corporation of Maryland Filed Oct. 3, 1956, Ser. No. 613,753

7 Claims. (Cl. 324-57) This invention `relates generallyto systems for testing electric signal transfer devices as, say, passive networks, vacuum tubes, transistors, or circuit stages such a amplilier stages. More particularly, this invention relates to testing systems of the sort described wherein an electric testing signal is applied to the input of such device to be transferred through the same, the testing signal after to produce by such differentiation a succession of signal` spikes of varying amplitude, and the presentation of such spikes as vertical deections in a cathode ray tube trace which is horizontally deected as a function of time. It is stated in the patent that such presentation will permit a check on the linearity of the amplifier.

The technique taught in the King patent is, however, characterized by a number of disadvantages among which are the following. First, while the height of any spike appearing on the screen of the cathode ray tube depends in part upon the noIIlineaI- response of the amplifier, this height also depends in part on the linear response of the amplifier, and, thus, it is impossible by inspection to readily dissociate the nonlinear response from the linear response. Accordingly, in the King technique it is necessary to resolve the height of the spikes into a linear component and a nonlinear component in order to determine the degree of nonlinearity.

Second, the discussed prior ait technique does not permit a determination, wi-th the sensitivity, which is desirable, of the nonlinearity or other electrical characteristics of the device being tested. Third, the presentation of the results of .the test -as a series of spikes rather than a continuous curve, complicates the interpretation of the presentation. Fouith, the staircase test signal which is used is characterized by high frequency components, and is thus not suitable for the testing'of devices as, say, some transformers or transistors, which will distort these high frequency components to thereby introduce a spurious frequency factor into the measure obtained, for the tested device, of a characteristic thereof which (like, say, nonlinearity) is not dependent on frequency.

It is accordingly an object of the invention to provide for testing of an electric signal transfer device in a manner whereby quantitative values obtained by the testing need not be resolved into components in order to permit formulation of a measure of a characteristic being tested for.

Another object of the invention is :to provide for testing of an electric signal transfer device in a manner whereby the measure obtained of a characteristic being tested for isi ameasure of improved sensitivity and accuracy.

A further object of the invention is to provide for testing of an electrical signal transfer device in a manner whereby the results obtained are, for easier interpretation, presented in the form of a continuousfunctional relation.

A still further object of the invention is to provide for testing of an electric signal transfer device in a manner whereby frequency distortion is minimized. g l

These and other objects are realized according to the invention by providing a source of testing signalsv of linear sawtooth waveform, differentiating means, and registering means which may be a cathode ray oscilloscope, and which is adapted to develop a trace or other observable indication representing a first input signal as a variable which is functionally related, as a dependent variable, to a second input signal supplied to the registering means. The mentioned sawtooth signal source is connected to an input of a signal transfer device to be tested such that the source supplies one or more linear Asawtooth signals to the said input. After passing through` the device to an output thereof, the sawtooth signals are differentiated by the differentiating means and are then applied, as the mentioned -lirst input signal, to the registering means. The second input signal for the registering means may be constituted of sawtooth signals taken directly from thementioned source, signals appearing at the mentioned output of the device under test, or some other signal whose variations, when correlated with the variations in the ldifferentiated signal, will permit a finding to be made concerning a characteristic of the device under test.

The Itesting system just described will, when operated, represent the differentiated signal as functionally related to the second input signal supplied to the `registering means. Such representation of the differentiated signal permits the formulation of a measure of a characteristic, such `as nonlinearity, of the `tested device without the necessity oflresolving quantitative values obtained in the results into separate components. As later described in more detail, the measure ywhich is obtained -is a measure of improved sensitivity ofthe Characteristic being tested for. The actually observed functional relation is presented in continuous form to thereby facilitate the interpretation thereof. As later described, lthe employment of a linear sawtooth signal as a testing signal permits testing of a signal transfer de vice in amanner whereby any frequency distortion of the test signal by the device can4 be minimized.

For a better understanding of the invention, reference is made to the following method and apparatus embodiments thereof and to the drawings which accompany the description and wherein: t l A Fig. l is a block diagram of one form of apparatus suitable for carrying out methods according to the pres ent invention;` p

Fig. 2` is a diagram of the output trace provided by the apparatus of Fig. 1; i i i Fig. 3 is a schematic diagram of a simple RC transfer network with the capacitor thereof shunted across the signal path;

Fig. 4 is a graph of the voltage response of the Fig. 3 network to a linear sawtooth signal as the duration t of the signal varies relative to the 'time constant T of the Fig. 3 network; l

Fig. 5 is a schematic diagram of a simple RC trans fer network with the capacitor thereof being connected in series with the signal path;`

Figs. A-GE, inclusive, are diagrams of indications ob tained by the apparatus of Fig. 1v under'ditfering test conditions;

Figs. 7 and 8 are detailed schematicdiagrams of cer'- tain circuits shown as blocks in Fig. l; and

V'Refelring to Pig. 1, an electrical unit 10 entitled sawto'oth circuits generates linear sawtooth signals which are supplied, first, by a lead 11 to a signal transfer device 12 to be tested, and, second, to a lead 13 which bypasses vthe device 12. The signal transfer device 12 may, assta'ted, be a passive network, a vacuum tube, a transistor, an lamplilier stage, or any other electric circuit component or system Vof components adapted to transfer an electric 'signal from 'an input of the vcomponent or component system to lan output of the component or component system.

An output of device 12 lis 'connected by a `lead 'l5 `to a fixed "contact 1'6. The *lead "13 is connected b'y a branch lead '17*to a 'fixed contact 18. A movable contact 19 may be manually thrown to selectively close with either the iiXed contact 16 or the fixed contact '13. Movable contact'19 is connected by lead 2o to 'the input of a unit 2l designated difrerentiator' and other circuits. Unit 21 includes a' means for differentiating the signal supplied thereto. This differentiating means may be of the elec- 'tronic `feed-'back type, but lfor most applications a simple RC 'difereutiator having a short time constant is completely satisfactory. The unit 21 may also include other circuits as later described.

The output signal from un-it 21 is applied by a Vlead 25 to the Y or vertical deflecting input 26 of acathode ray oscilloscope l27 provided with aDaC. 'vertical deflecting -amplien Thehorizontal dellecting signal for the oscilloscope may *be provided, as shown in Fig. l, by connecting the llead V13 to the X horizontal deflecting .input i2l? of the oscilloscope. If desired, however, other .horizontal deflecting signals .may be used, as, say, the signal appearing ,at the output :of the device 142.

WEigs. 7 yand 8 show details of the velectric units 10 and .21 .represented in block form Fig. .1.. :In the unit 'lil A(.ig. 7) an alternatingrsignal .of well .regulated .frequency (as, say, Aa signal derived vfrom a `6O-cycle power line) is passed through `a transformer 30 to a pulse shaping circuit which `is comprised of a resistor 31 and a gas tube 32 ein series, and which serves .to give a generally square waveform to the signal. The square Waveform signal is differentiated `by the series combination of capacitor 33 and .resistor 34 to produce positive triggering pulses which are applied to the `grid `35 of the normally cut-off, lefthand triode section 36 of a vacuum tube 37 whose left and right-hand triode sections 36, .38 are connected in circuit withassociat'ed resistors and capacitors .to form amonostable multivibrator.

The negative square wave output of the .multivibrator is supplied Yvia `lead 39 to the grid 40 of va triode 41 which normally draws plate current through the series path of diode 42, resistor 43, junction 44, and .resistor l45. A capacitor 46, a junction 47, a capacitor 48, andlaresistor 49 are connected .inseries between the junction 44 and the cathode .of ytube 41. The negative square 'wave applied to grid 40 cuts ofi triode 41 to produce charging of capacitors 46, 448 -to thereby cause va sawtooth voltage to appear between junction 44 and ground.

The 'sawtooth voltage, .in -ord'er to vimprove the linearity thereof, .is-'supplied -to the grid 50 `'of a cathodefollower tube 51 whose output is supplied to junction 47 through a variable'resistor .52, and 'whose output is also supplied to the ,junction `of -tube 42 and resistor 43 through the capacitor 53. The'couplings just-described cause the output of cathode follower 51 to act as aregencrative .feedback signal 'which renders substantially vlinear the sawtooth voltage vdeveloped at junction 44. The .diode 42 is an isolating diode used to prevent this regenerative feedback vsignal Afrom being fed :back :to .the .power supply. Another 'diode 54 is, for .DnC. :recovery purposes, Iconnected between junction 47 and the output of fc'athod'e l follower tube 51.

resistors 518,259, 60 to act as a phase splitter. lhesepa- 4 ratte outputs of the phase-splitter tube 57 are coupled through the capacitors `65, 66 to the fixed contacts 67, 68 of a switch 69 having a movable contact 70. The D.C. restorer diodes 71, 72 are connected, respectively, to the junctions of capacitors 65, 66 with contacts 67, 68 in order to facilitate rapid discharge of the capacitors 65, 66 following each charging thereof by a sawtooth signal.

The movable-contact 7:0 of `switch 69 is manually operable to selectively yclose with 'either the fixed contact 67 or the fixed contact `68. 'By selectively closing contact 'tl with, respectively, the iixed contact 67 and the lined contact 68, it is Apossible to produce at the output of unit 10 a sawtooth signal which 'rises in voltage during its duration anda sawtooth signal which falls in voltage during the duration thereof. 1

The movable contact '70 is connected to the grid 75 of a cathode follower tube 76 whose output is connected to the lead 13 which is shown (Fig. l) as supplying the horizontal deectling signal for the voscilloscope 27. An output attenuator 77 (Fig. 7) is connected between the lead 13 and ground. The lead 11 is selectively connectable'to various ,taps on the attenuator 77 to thereby provide selectivity `in the amplitude of sawtooth signal 'supplied by lead 1l to the device 12 (Fig. l).

In the unit 21, the input signals received thereby on lead 2i) (Figs. l and 8) may be selectively attenuated vby a potentiometer (Fig. 8) consisting of a resistor Si) and a tap 81 which rides on the resistor. From the tap 81, the signals are passed through a cathode followerl `32 to a differentiating circuit constituted of the capacitor 83 and the resistor 84. The differentiated signal which results from this circuit is amplified in a tube 85 to be thereafter supplied to the input of a phase-splitted tube 86. The separate phase-split outputs of this tube are supplied through the capacitors 87, l88 to, respectively, the fixed contacts 89, 9i) oa .switch 91 .having a movable Acontact `92. By manually operating movable contact 92 to selectively close with either 'fixed con-tact 89 or with fixed contact 96, it lis possible to reverse'the polarity ofthe differentiated signal so that, whether the sawtooth signal applied to device 12 is positive-going or negative-going, Ythe trace developed on the screen of the oscilloscope 27 (Fig.

l) in the presence of the differentiated signal is,` say,

upwardly displaced from the path followed by the .trace when zero signalv is applied .to the Vertical deecting input 26. The signal appearing on movable contact 92 is passed through -a .final cathodeV follower tube 93 to be applied to thelead25 `whichfurnishes (.Fig. 1)-the vertical deilectingsignalfor .the oscilloscope 27. Y

Considering now the operational 'characteristics of a system according tov the `present invention, :the sawtooth signal source should be capable yof providing sawtooth `output Asignals whose amplitude will cover the dynamic range of .interest 'of the device 412 being tested. Moreover, the linearity -of the sawtooth signals should be as .high .as possible, and, 'in any event, should `be substantially greater than v.the expected degree lof linearity of the device being tested. -When the device 12 draws considerable power, it is kdesirable to so `operate the sawtooth unit 10 that the unit has a Alow-.duty cycle. The advantage of :such .low-.duty cycle is that it permits Ameasurements to be -made Ausing peak amplitudes which would cause excessive dissipation under steady :state lconfditions. 1

.AS .a preliminary to actual testing .of the device 12, it is Voften desirable to determine the-device 12 loads lthe sawtooth-.unit .1'0fto an undue degree. ln `iurtherance of this determination, .themovable contact 19 (Fig. l)

is thrown to 'close with the .fixed contact `13 to supply Athe sawtooth signals ffrorn unit A11i] Yas the input signal tothe diterentiator unit 21. Next, the @device .12 :is disconnected from sav/'tooth unit il), and, under these-conditions "a trace is 'developed `on 'the oscilloscope. The ltrace so obtained represents the-differentiated form of fthe sawtooth signal Ltrotn :the aawtooth unit i when no'floadin'g is impressed thereon. The device 12 is then reconnected to sawtooth unit with movable contact 19 being kept closed with xed contact 18. Under theseI last-named conditions, the trace which is obtained represents the differentiated output of sawtooth unit 10 when loaded by device 12. The absence of any substantial difference in shape between the latterly-obtained trace and the formerly-obtained trace indicates that the device 12 does not load the sawtooth unit A10 unduly so as to introduce an error in the results obtained bythe measurement procedure aboutto be described.`

As a second preliminary, the movablecontact 19 is thrown to a position midway between xed contacts 16, 18 (so that zero signal is supplied to the Y input 26 of oscilloscope 27), and the path of the horizontal trace, which then appears on the screen of the oscilloscope, is marked or otherwise noted. This path, which is represented in Fig. 2 `by zthe line 98, represents the base line to which the trace is referred during the testing of the device 12,.

To test device 12 with positive-going signals, the movable contact 70 `of switch 69 (Fig. 7) is closed with xed contact 68 to apply sawtooth signals of rising amplitude to the device 12. Also, the movable contact 92 of switch 91 (Fig. 8) is thrown to close with the appropriate one of the fixed contacts 89, 90 which will cause the trace developed in the presence of the differentiated signal to be upwardly displaced from the base line 98.

Next, the movable contact 19 is thrown to close with ixedcontactlto thereby couple the output of device 12 to the input of dierentiator unit 21. In this circumstance, a trace 100 (Fig. 2) appearing on oscilloscope 27 will represent the derivative of the output signal from device 12 with respect to time in terms of the vertical displacement 99 of the trace from the 4base line 98. If the device 12 has a linear response to the sawtooth signals from unit 10, the value of this derivative will be constant, and the trace on oscilloscope 27 will accordingly appear as a straight horizontal line. If, on the other hand, the device 12 responds nonlinearly tothe sawtooth signals, the mentioned derivative will vary in value, and the trace on the oscilloscope will accordingly be characterized by a vertical deviation from its initial horizontal placement 99) which areused to determine degreeof non-linearity are horizontally displaced on the`osci11oscope screen to thereby permit convenient separate observations ofthe two responses. By virtue of this horizontal displacement, a measure of the degree of nonlinearity of device 12 may be obtained without first having to resolve a vertical displacement value of the trace at a given lhorizontal point into ytwo components (corresponding to, 99 and 101) in order to obtain the measure of nonlinearity., l t

` The procedure just described tests the device 12 with positive-going sawtooth signals. It may also be desirable to test device l2 with negative-going sawtooth signals inasmuch as the response of the device to negative- Vgoing lsignals may not be the same as with positive-going signals. To test with negative-going signals, the movable contact 70 in sawtooth unit 10 (Fig. 7) is thrown to close with fixed contact 67 to cause negative-going sawtooth signals to appear at the output of the unit. In

these circumstances, the horizontal sweep .of the trace of oscilloscope 27 Yis from right to left, and the .test

signals applied tddevice '12 are negative-going signals.

If the device 12 is nonlinear, and if movable contact 92 (Fig. 8) is still maintained in the position used therefor when testing with positive-going signals, the trace will be displaced downwardly rather than upwardly of the base line 98. For better comparison, however, of testsmade with positive-going signals and of tests made with negative-going signals, it is desirable that the trace be displaced upwardly of the base line in each instance. This upward displacement ofthe trace may be obtained'in the case of testing with negative-going signals by throwing movable contact 92 (Fig. 8) in diiferentiator unit 21 to occupy the closed position which is opposite that occupiedby the said movable contact when used during testingof device 12 by positive-going signals.,

The results of the testing of a given device 12 with both positive-going sawtooth signals and negative-going sawtooth signals can be presented on the screen of t the oscilloscope in a convenient manner by using the horizontal trace centering control of this instrument Vto bring the starting position of the trace to the horizontal center of the screen, and by then testing the device first with positive-going signals and then with negative-going signals in the manner already described.

In some instances, it will be found that the vertical deviation 101 (Fig. 2) of the trace 100 may be so small as to not be yreadily observable. Y This diiculty may easily be remedied by increasing the vertical gain of the oscilloscope 27 by `a known factor, and Eby then using the ventical centering control of the oscilloscope to bring the: trace back Ato` a vertical positionwhich `is observable on the screen.

As stated, one of the principal uses of the described system is to provide a measure of the degree of nonlinearity of a signal transfer device.` The conceptY of distortion expressed in terms of degree of nonlinearity,1 isnuot as familiar as that of distortion expressed in terms of harmonic content. Therefore, a quantitative comparison will be made between the results obtained with a generalized nonlinear device, using the described method and the results obtained with the method of harmonic analyses.

Consider a nonlinear device 12 whose characteristics can be expressed by the powerseries (3) y y=akr+k2r+ck+nke4+ and the derivativeof the `output with respect to t is A measure of the linearity can now be made byl com- Y, paring the magnitude of the first term with the remaining terms. This is done by taking the ratio ofthe value represented by the vertical deviation 101 at time T ofthe trace from its original horizontal path to the value represented by the vertical displacement 99 of trace 100 from `base line 98 at the start of the trace. Such ratio, which will be called the departure is given by the following equation.

where ggg .t a0, .t .a T

and, where veach of the terms an A etc. is considered a component of departure from linearity.

Equation I `shows that the total departure at t=T is a weighted sum of distortion components whose coefcients are B/A, C/A, D/A, etc. Theoretically, the magnitude of each coefficient can be computed by deriving the equation ofthe curve of Figure 2. Practically, this `becomes increasingly dicult las the order of the curvature increases and in lieu thereof .it has :been -found more satisfactory, according Lto the present invention, to use, 'as a `measure of nonlinearity a iigure of demerit which weights the various distortion coefficients. This figure corresponds to the right-hand expression in Equation 5. As already indicated, and as shown =by Fig. 2, the Value of the gure of demerit can V.be obtained by dividing the vertical deflection 101 of the trace from its original horizontal path by the vertical displacement 99 of the vtrace from the base line 98.

Consider now the results obtained when .the method of harmonic .analysis is used. According to this last-.named method, if 1a sinusoidal waveform, having -a peak amplitude of kt, is introduced into the same device the input is given as Y (6) x=`kT sin wt and .the output will be y=AkT sin -wt-i-BkzT2 sin2 wt -l-Ck-3T3 sin3 tot-'l-Dk4T4 sin* tut-land expanding each .term gives A direct Ycomparison with Equation 5 can now be made on a term by term basis. Considering the second harmonic (in the second term` of Equation 8), the ratio of the second harmonic component to that of the fundamental is Y Y Y 9 Second harmonio BkT 1Fimdamental 2A From EquationrS, the departureat .time I=Tis-given by .2li/ ir M :g1-3H for the eeeon'rl Aorder component .of

l A departure from linearity to Comparing the right-hand expressions .ofEquations 9 and V10 it will 'be seen that departure as herein dened provides a more sensitive measure of second harmonic distortion than is obtained by expressingthis distortionas From actual operating data, it has been observed that a departure of 0.01 is readily detected, making it completely feasible to detect la second Aharmonic whose amplitude .is only 0.025% of the fundamental.

.A comparison of the higher order terms respectively obtained with `the nonlinearity and harmonic analysis methods shows an even Vgreater sensitivity .advantagefor the method of using components of departure from linearity ascontrasted to the methodof harmonic analysis. For the third and fourth terms the ratio of linearity departure to harmonic amplitude is 12 and 32, respectively.

The discussion thus far has 'been limited to a nonlinear device which exhibits no frequency distortion. In applications of the nonlinear'ity method it is desirable to use a repetitive Waveform, and it is important to knowv the bandwidth requirements for the particular waveform selected. The necessary bandwidth will be a'function-.of the degree of precision which is sought.

A simple Fourier analysis of the repetitive sawtcoth is not applicable because much of the harmonic content is associated with the sharp trailing edge which is of 'no' consequence for the purposes at hand. Therefore, the analysis will be made using ya ramp function in conjunction with several .elementary low and .high pass filters. Considering `first the low pass .circuit .fof-Fig. 3, :the transfer function is Figure .4 is a plot of Equation 12. When tSAT, the departure from linearity ;of the sawtooth -is less than 9.0.1. If the `initial portion of the sweep is of interest, it is necessary to use :a sweep of sufcient duration to permit Athe .error to drop tov the required limit during theearly portion yof the sweep. .In most applications the nonlinear- 1ty `occurs at the higher amplitudes and `-the high frequency attennatlon `is lof lesser importance than the low v-freqnency distortion.

For the :high pass circuit of Fig. '5, the transfer A `function `is given by and .the transform .of `theoutputis .(11.3) f one=ggz and (14) 'ema-.kTQ-e-t/T) Equation 1.4 is similar to the familiar eiipression .for

vthe current in an RL circuit with a step v.function input.

If t=0.02T the departure from linearity is less .than `07.01.

The analysis of the Fig. .5 circuit also indicates, with respect to the RC `diterentiator .circuit in unit 101hat the time constant thereof -must be short ,enoughto permit the derivative of the waveform to rise towithin ,afsmall l percentage of vthe nal value in a time .short compared with the sweep time. fAs an example, if the derivative '.is to reach 98% of the final value in the :first 5% of a 1 millisecondsweep, then there may be set nprfromthese Afigures the `simultaneous :equations:

aceites' t/ T=3.9 t T= 14.7 microseconds The analysis of the two elementary networks indicates the degree to which a poor low frequency response (Fig. network), distorts the latter portion of the waveform and an inadequate high frequency response (Fig. 3 networflc) distorts the initial portion. Since such networks are ,illustrative of what may be expected in the way of frequency response in signal transfer devices of more complex circuitry, it is necessary to determine the distortion` of the output waveform by the bandwidth limitations `of the device under test.

., Due to the number of conditions involved, `a trial and error approach is convenient in determining if a given sweep duration for the sawtooth signal is appropriate for use with a particular device 12 to be tested. Thus a sweep duration is arbitrarily selected, and the bandwidth of the device to be tested computed for a given precision. If the bandwidth of the device is suiiicient but not coincident with that of the waveform, the sweep duration can be altered. If the bandwidth of the device is not sutlicient, the precision will suffer.

i Several examples of presentations which may be expected are shown in Figs. 6A-6E wherein the line 102 is a vertical center line for the oscilloscope screen and wherein the trace 100 is a composite trace having righthand and left-hand components which each start at line 102, and which respectively represent the results of testing with positive-going andY negative-going signals in the manner already described; The first illustration (Fig. 6A) represents a device having a gain which varies linearly with signal. Fig. 6B is typical of an amplifier which is being overloaded symmetrically and Fig.6C shows an asymmetry indicating that distortion is occurring more rapidly for the positive portion of the cycle. Figs. 6D.` and E'indicate the results which would be obtained with devices having insuiicient bandwidth. A rapid method for determining whether distortion is due to amplitude or frequency limitations is to drastically reduce the amplitude of the sawtooth. If` this does'not result in a change of shape the effect is naturally due to inadequate bandwidth.

The comparison which has been made above between the nonlinearity and harmonic analysis methods of measuring distortion demonstrates that the former (nonlinearity method) weights the various coeiicients of distortion B/A, C/A etc. in order to provide a measure of total distortion, whereas the harmonic analysis method of summing the harmonic amplitudes does not make any allowance for weighting the various harmonics. This fact of a weighting of distortion coeicients in the manner described by the nonlinearity method renders ythis method advantageous compared to the harmonic analysis method inasmuch as it has been found, because of this weighting, that the results obtained with the nonlinean'ty method are a better measure of, say, the amount of distortion which appears present -to the ear in sonic reproduction, than are the results obtained with the non-weighting harmonic analysis method.

While the foregoing description has dealt with testing for nonlinearity, the described testing system is useful also in the determination of the dynamic gain of an ampliier, transconductance of a vacuum tube, dynamic current gain of a transistor (alpha or beta), or any other characteristic which is determined by taking the partial derivative of one electrical quantity with respect to another electrical quantity.

In the case of dynamic gain of an amplifier, for example, assume that v represents the input voltage and u Y '10 represents the output voltage. Then the dynamic gain is given by the expression:

Suppose now that we apply to the input of an amplifier 12 from unit 10 a sawtooth signal having a voltage v equal to kt, where t is time and k is a constant. The output voltage .u from the amplifier will vary as a function of time, and this output voltage isrdiiferentiated by diierentiator unit 21 to render the vertical displacement of the trace from the base line 98 representative of the value The plot so obtained is readable in terms of the dynamic gain A in accordance with the following considerations. By taking the partial diierential of both sides of the below expression we get (17) ev=ker Substituting kt from (17) for 6v in (15), there is obtained :Expression 19 indicates that the vertical displacement of the trace 100 from base line 98, is at any time t representative of the instantaneous gain A multiplied bythe factor k. Once the factor k is determined,1which can be done by computation or measurement, the vertical displacements of the trace can readily be converted into values of A. Moreover, once the factor k is determined, the times t at which vertical displacements of trace 100 are read ot can, from Expression 16, be converted into values of the input voltage v. Accordingly, the trace 100 which is obtained can be treated as a plot of the variation in dynamic gain A of the tested ampjlier as the input voltage v to the amplifier is varied. If desired, the vertical and horizontal gain of the oscilloscope may be adjusted to render the trace a plot of A as a function of v which can be directly read off the scales used to measure vertical and horizontal displacements on the screen of the oscilloscope.

In like manner, other electrical characteristics which are deined as the partial derivative of a first electrical quantity (dependent variable) with respect to a second electrical quantity (independent variable) can be determined by (l) linearly varying the iirst quantity with re spect to time and using the rst quantity as an input signal to produce the second quantity as an output signal,.

(Z) electrically diierentiating the output signal so as to obtain the partial derivative thereof with respect to time, (3) electrically plotting the variations in time of the diierentiated signal.

For example, if a triode 12a is connected as shown in Fig. 9 so that a sawtooth voltage signal is applied to the grid of the triode, a substantially constant plate voltage is impressed on the tube from the battery 110, and a small value resistor 111 is interposed in the plate circuit of the tube to convert current therein into a voltage which Ais .thereafter diterentiated by iuuit 2J, than the trace obtained on oscilloscope .27 can `be".,ennsi'deied a plot o-f gm, the partial derivative of plate current with respect to grid voltage as-the plate voltage stays constant. As another example, if aitransistor 12b is connected as .showuin Fig.. ..10 4so ,theta .sawtcoth v-current Signal is aptiled .to the vhase e1eetr0de,rand.so thatalcw value .re- Sister 112 .is connected between the 'collector and a source '1.13 .of veltagelof constant value to .Convert Vthe conector Ycurrent into a voltage which. is `'differentiated .by unit f2.1, then the trace obtained .on oscilloscope 27 can .be .considered a plot of ,'(beta), the partial de rivative of the collector current with respect to base current as the collector voltage stays constant.

The above-described method and apparatus embodiments being exemplary only, it will be understood that the Present invention eoxapreheuds embodiments differing in form or detail from the above-described embodiments. Accordingly, the linvention is not to be considered as limited save as is-consonant with the scope of thetfollowing claims.

I claim:

l. vApparatus tfor measuring an V.electrical characteristie o-fa device adapted to transfer '2L-.Signal from en, input thereof to can; output thereof, .saideapparatus comprising, a source of linear sawtooth signals,v rneans tocouple said signals -to said inputfor transfer through said device to said output, diiferentiator means coupled to said outp-ut to differentiate the signal thereat, and means to register the time variations iin-amplitude of said diiferentiated sign.

2. Apparatus for-measuringan electricalcharacteristic of a device adapted to transfer a signal from anrinput thereof to an output thereof, said apparatus comprising a source of linear sawtooth signals, means to couple said signals to said input for transfer through said device to said output, a diierentiator circuit coupled to said ofutput -to differentiate the signal thereat, a cathode ray oscilloscope respectively responsive to irst and second input signals thereto to produce respective deilections of ,a Vtrace .inrespective directions .at right angles .to reach other, means tosupply the differentiated; signals from said circuit assaidrst input signal'to said oscilloscope, and means to.supply asignal which ,has ia predeterminedrelation in amplitude `to :said sawtooth fsignals as said second input signal. to-said oscilloscope.

3. Apparatus as in claim 2 wherein said diiferentiatpr circuit is comprised of resistance means and capacitance means in series. i

4. Apparatus as in claim 3 wherein saidtliffereritiator circuit has a short time constant relative to the durations of said sawtoothsignals.

y 5. Apparatus as in claim 2 wherein said sawtgoth signals Yare supplied as said `second input signal to said oscilloscope. Y l i 6. Apparatus -for measuring 'an Velectrical characteristic of a device adapted to transfer a signal frornan input thereof` to an output thereof, said apparatus comprising, a source ofV linearv sawtooth signals, means `to reverse the polarity o'f lsaid sawtooth signals, Y`means Vto couple said signalsto said input for transfer through said device VVto said output, afdiferentiator circuit'coupledtoy said output to differentiate the signal thereat, a cathode ;ray oscillof scope respectiveiy responsive'to rst and second 'inputsignals etheretoto t produce respective deflections -of a trace in respective directions at'right angles to each 'other-means to fsupply the-differentiated signals from said circuit as said irst input signal'to said oscilloscope,-means-toreverse the polarityof said differentiated signals supplied-'to said oscilloscope, and means: to supply said sawtoothsign-als as saidsecondinput-signalto said oscilloscope.

7. Apparatus `aslin cla-im A6 `further comprising switch means to selectively couple the input'ofsaid'ditferentiator circuit .to said output of said device -andvtosaid source of sawtooth signals.

:References Cited inthe tile .of this patent UNITED STATES -PA'TENTS 

